Mohammad Moulaeifard , Florian Wellmann , Miguel de la Varga, David Bommes

Methods from the field of Computer Graphics are the foundation for the representation of geological structures in the form of geological models. However, as many of these methods have been developed for other types of applications, some of the requirements for the representation of geological features may not be considered and the capacities and limitations of different algorithms are not always evident. In this work, we, therefore, review surface-based geological modelling methods from both a geological and computer graphics perspective. Specifically, we investigate the use of NURBS (Non-Uniform Rational B-Splines) and subdivision surfaces, as two main parametric surface-based modelling methods, and compare the strengths and weaknesses of both approaches. Although NURBS surfaces have been used in geological modelling, subdivision surfaces as a standard method in the animation and gaming industries have so far received little attention – even if subdivision surfaces support arbitrary topologies and watertight modelling, two aspects that make them an appealing choice for complex geological modelling. Watertight modelling is a type of modelling in which the surfaces of the model have sealed interactions with all surrounding surfaces, resulting in the generation of closed volumes. Watertight models are, therefore, an important basis for subsequent process simulations based on these models.
Many complex geological structures require a combination of smooth and sharp edges. Investigating subdivision schemes with semi-sharp creases is therefore an important part of this paper, as semi-sharp creases characterize the resistance of a mesh structure to the subdivision procedure. Moreover, non-manifold topologies, as a challenging concept in complex geological and reservoir modelling, are explored, and the subdivision surface method, which is compatible with non-manifold topology is described.
Finally, solving inverse problems by fitting the smooth surfaces to complex geological structures is investigated with a case study. The fitted surfaces are watertight, controllable with control points, and topologically similar to the main geological structure. Also, the fitted model can reduce the cost of modelling and simulation by using a reduced number of vertices in comparison to the complex geological structure.